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Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm? |
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Answer» Let the time taken by pipe to fill vessel = t minutes Since water flows 10 m in 1 minute, it will flow 10t meters in t minutes. According to the question, Volume of conical vessel = Volume of water that passes through pipe in t minutes Consider conical pope Base Diameter = 40 cm Base radius, r = 20 cm Height, h = 24 cm We know that the volume of cone = 1/3πr2h Volume of conical vessel = 1/3π(20)2(24) = 3200 π cm3 Consider cylindrical pipe Base diameter = 5 mm = 0.5 cm Base radius, r = 0.25 cm Water covers 10t m distance in pipe, Hence, we get, Height, h = 10t m = 1000t cm We also know that, Volume of a cylinder = πr2h Volume of water passed in pipe = π(0.25)2(1000t) = 62.5tπ cm3 So, we have 62.5tπ = 3200 62.5t = 3200 t = 51.2 minutes We know that, 0.2 minutes = 0.2(60) seconds = 12 seconds Therefore, t = 51 minutes 12 seconds |
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